Finite Group Databasebeta

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C11×C19×C3⋊Dic15 #49178482

order37620
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C3

Aliases

direct productC11×C19×C3⋊Dic15
unambiguous semidirect productC3⋊(C11×C19×Dic15)

Splittings

derived, HallC32×C5 ⋊ C4×C11×C19
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ C3⋊Dic3
HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C19
HallC32×C19 ⋊ C11×Dic5
HallC32×C11 ⋊ C19×Dic5
HallC5×C19 ⋊ C11×C3⋊Dic3
HallC5×C11 ⋊ C19×C3⋊Dic3
SylowC32 ⋊ C11×C19×Dic5
SylowC5 ⋊ C11×C19×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C11×C19C3⋊D15
commutator, hypocenterC32×C5C4×C11×C19
FrattiniC2C11×C19×C3⋊D15
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C32×C5C2×C11×C19
LCSG ▷ C32×C5
UCSC1 ◁ C2×C11×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

10032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 191);